Creeping Convection in a Horizontally HeatedEllipsoid

G. D. McBain

Memjet Australia Pty LtdNorth Ryde, NSW

Twentieth Australasian Fluid Mechanics ConferencePerth, 2016

Natural convection in side-heated cavities

Spherical cavities (McBain 2001)

Ellipsoidal cavities

Temperature in the surrounding solid

Zeroth-order temperature in the cavity

Creeping convection in rectangle (Batchelor 1954)

Stream-lines in an ellipse

Forced flow in elliptic duct (Mathieu 1853)

Pressure in side-heated ellipse

Pressure in side-heated sphere (McBain 2001)

Buoyant flow in elliptic duct (McBain 1999)

Creeping solution for ellipsoid

First-order correction to temperature

Temperature to first order

Ra = 103

Ra = 104

Ra = 105